Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 2100 miles, for a total gas consumption of 65 gallons. How many gallons were consumed by each of the two cars that week?

A Family Has Two Cars The First Car Has A Fuel Efficiency Of 40 Miles Per Gallon Of Gas And The Second Has A Fuel Efficiency Of 20 Miles Per Gallon Of Gas Durin class=

Sagot :

Answers:

  • First car =   40    gallons
  • Second car =    25     gallons

==========================================================

Explanation:

I'll denote the cars with the labels A and B.

Car A has a fuel rating of 40 mpg (miles per gallon) and car B gets 20 mpg.

Let,

  • x = number of gallons used by car A
  • y = number of gallons used by car B

Since car A gets 40 mpg, and uses up x gallons, then it travels 40x miles. Multiply the fuel rating with the number of gallons used to determine the distance traveled. Car B travels 20y miles since it gets 20 mpg.

Overall, the two cars travel a combined distance of 40x+20y miles. This is set equal to the 2100 miles stated to form the equation 40x+20y = 2100.

Let's divided every term by 20

40x+20y = 2100

40x/20+20y/20 = 2100/20

2x+y = 105

Then isolate y to get

y = 105-2x

We'll use this equation later.

------------------------

The two cars use up a total of 65 gallons, which means,

x+y = 65

Then we'll plug in y = 105-2x and solve for x.

x+y = 65

x+105-2x = 65

-x+105 = 65

-x = 65-105

-x = -40

x = 40

Car A (the 40 mpg car) used 40 gallons. It traveled 40x = 40*40 = 1600 miles.

Car B (the 20 mpg car) used y = 105-2x = 105-2*40 = 25 gallons of gas. Or you could note that if x = 40, then x+y = 65 must lead to y = 25. It traveled 20y = 20*25 = 500 miles.

The two cars combined distance is 1600+500 = 2100 miles to help verify the answers.

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.